The suppressed decay chain B{sup -}{yields}DK{sup -}, D{yields}K{sup +}{pi}{sup -}, where D indicates a D{sup 0} or D{sup 0} state, provides important information on the CP-violating angle {phi}{sub 3}. We measure the ratio R{sub DK} of the decay rates to the favored mode B{sup -}{yields}DK{sup -}, D{yields}K{sup -}{pi}{sup +} to be R{sub DK}=1.63{sub -0.41}{sup +0.44}(stat){sub -0.13}{sup +0.07}(syst)x10{sup -2}, which indicates the first evidence of the signal with a significance of 4.1{sigma}. We also measure the asymmetry A{sub DK} between the charge-conjugate decays to be A{sub DK}=-0.39{sub -0.28}{sup +0.26}(stat){sub -0.03}{sup +0.04}(syst). The results are based on the full 772x10{sup 6} BB pair data sample collected at the {Upsilon}(4S) resonance with the Belle detector.